How could I as a greencard holder be able to apply for citizenship if I work in my home country of Jamaica?

Your facts suggest that you may have abandoned your residency.   If you have been outside the U.S. longer than 180 days but less than a year, there is a rebuttable presumption that you have abandoned your residency and you will need to prove, with documentary evidence, that you have not abandoned residency. If you have been outside the U.S. longer than 1 year, you have abandoned your residency and upon entry into the U.S., you should seek to see an Immigration Judge and then hire competent, experienced counsel to defend you in removal proceedings. Typically, a Lawful Permanent Resident who knows that they will be abroad longer than 180 days should apply for a re-entry permit, which is valid for 2 years.   Please consult with an immigration attorney about your predicament.